For an apparatus (facility) converting fuel to at least kinetic energy, thermal energy, or electrical energy, which is represented by a cogeneration apparatus, there is a technique of Condition Based Maintenance (CBM) in which a plurality of sensors (measuring instruments) for measuring the state is provided to measure and recognize each state of the apparatus every second, judge normality or anomaly in the state of the apparatus based on its data (referred to as apparatus state measurement data (state data), sensor data, or others), take an anomalous state, and perform maintenance. This is effective for reducing a maintenance cost.
Japanese Patent Application Laid-Open Publication No. 2002-110493 (Patent Document 1) and Japanese Patent Application Laid-Open Publication No. 2000-252180 (Patent Document 2) describe a method of multistage multivariate analysis which repeats an operation in multi stages, the operation for quality-variation cause analysis in a manufacturing line, in which a plurality of explanatory variables are divided into a certain small number, linear multiple regression model creation (Yi=A·Xi) is applied to all divided groups, the explanatory variable is narrowed down in each divided group by a forward selection method, and the narrowed-down explanatory variables are combined together to apply the multiple regression model creation again.
U.S. Pat. No. 7,209,846 (U.S. Pat. No. 7,209,846 B2) (Patent Document 3) describes a method of a causation analysis between a product quality and a process data in a manufacturing line with using a graphical model.
Non-Patent Document 1 describes a statistical model. More specifically, it describes a GLM (Generalized Linear Model) method, a GAM (Generalized Additive Model) method, and a non-linear model method.
Non-Patent Document 2 describes a plurality of methods of creating a degenerate linear regression model (Y=A·X) for an objective variable (Y) and an explanatory variable (X) based on a Projection Method for avoiding a non-computable problem and insufficient accuracy due to a Multiple Co-linear phenomenon caused by simultaneous shift of a plurality of elements of the explanatory variable. More specifically, it describes a PLS (Partial Least Squares) method, a PCR (Principal Component Regression) method, a Ridge method, and a Lasso method. Also, as a method of creating a nonlinear-relation model, it describes a nonlinear regression method. More specifically, it describes a GLM (Generalized Linear Model) method and a MARS (Multivariate Adaptive Regression Splines) method.
Non-Patent Document 3 describes a method of constructing a linear regression prediction model by mixing collinear data items with using a PLS (Partial Least Squares) method.
Non-Patent Document 4 describes a method of a statistical-mathematical general-purpose algorithm for a causation analysis with using a graphical model.
Non-Patent Document 5 describes a method of computing a lifetime of a part with using a proportional hazards model and a logistic regression model which is one type of the GLM.    Patent Document 1: Japanese Patent Application Laid-Open Publication No. 2002-110493    Patent Document 2: Japanese Patent Application Laid-Open Publication No. 2000-252180    Patent Document 3: U.S. Pat. No. 7,209,846 (U.S. Pat. No. 7,209,846 B2)    Non-Patent Document 1: ISBN: 978-0412830402 J. M. Chambers, and T. J. Hastie, “Statistical Models in S”, Chapman & Hall/CRC (1991), Chapter 6: Generalized Linear Models, Chapter 7: Generalized Additive Models, Chapter 10: Nonlinear Models    Non-Patent Document 2: ISBN: 978-0387952840 T. Hastie, R. Tibshirani, and J. H. Friedman, “The Elements of Statistical Learning”, Springer (2003), Chapter 3: Linear Methods for Regression    Non-Patent Document 3: ISBN: 0-471-48978-6, Richard G. Brereton, “Chemometrics, Data Analysis for the Laboratory and Chemical Plant”, WILEY (2003), Chapter 5: 5.5 Partial Least Squares    Non-Patent Document 4: ISBN: 978-0387310732 Christopher M. Bishop, “Pattern Recognition and Machine Learning”, Springer (2006), Chapter 8: Graphical Models    Non-Patent Document 5: Haitao Liao, Wenbiao Zhao, and Huairui Guo, “Predicting remaining useful life of an individual unit using proportional hazards model and logistic regression model”, IEEE RAMS '06, Annual Reliability and Maintainability Symposium, 2006. pp. 127-132